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       <article class="full-content post-2101 post type-post status-publish format-standard hentry category-63 category-61 category-84 category-3 tag-andrew-gelman tag-bayesian tag-frequentist tag-larry-wasserman tag-nate-silver tag-the-signal-and-the-noise category-63-id category-61-id category-84-id category-3-id post-seq-1 post-parity-odd meta-position-corners fix" id="post-2101">
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           <a class="entry-title" href="http://blog.cos.name/taoshi/2012/12/07/frequentist-or-bayesian/" rel="bookmark" title="大话统计：Frequentist or Bayesian">
            大话统计：Frequentist or Bayesian
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            <a href="http://blog.cos.name/taoshi/category/%e5%aa%92%e4%bd%93%e6%8a%a5%e9%81%93/" rel="category tag">
             媒体报道
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            <a href="http://blog.cos.name/taoshi/category/%e6%95%b0%e6%8d%ae%e5%88%86%e6%9e%90/" rel="category tag">
             数据分析
            </a>
            ,
            <a href="http://blog.cos.name/taoshi/category/%e7%bb%9f%e8%ae%a1/" rel="category tag">
             统计
            </a>
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             闲扯
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           12月
          </span>
          <span class="day">
           07
          </span>
          <span class="year">
           2012
          </span>
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        <span class="updated" title="2012-12-07T10:58:34+00:00">
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          <p>
           [前言：先向无法科学上网的客官作揖抱歉了，有些江湖野史可能被墙]
          </p>
          <p>
           话说江湖风云人物，神算子
           <a href="http://en.wikipedia.org/wiki/Nate_Silver" target="_blank">
            Nate Silver
           </a>
           ， 在纽约时报
           <a href="http://fivethirtyeight.blogs.nytimes.com" target="_blank">
            开博占卜
           </a>
           各项江湖话题，每每言中。并著书立传，
           <a href="http://www.us.penguingroup.com/static/pages/features/the_signal_and_the_noise.html" title="The Signal and the Noise - Books by Nate Silver - Penguin Group (USA)">
            The Signal and the Noise
           </a>
           ，一时引来
           <a href="http://cos.name/2012/11/the-rise-of-data-scientists/" target="_blank">
            各相追捧
           </a>
           。
          </p>
          <p>
           这日，曾留下武林秘籍
           <a href="http://www.amazon.com/All-Statistics-Statistical-Inference-Springer/dp/0387402721/" target="_blank">
            All of Statistics: A Concise Course in Statistical Inference
           </a>
           的大侠
           <a href="http://www.stat.cmu.edu/~larry/" target="_blank">
            Larry Wasserman
           </a>
           (Department of Statistics, Department of Machine Learning, Carnegie Mellon University) 突发感想，在自己博客
           <a href="http://normaldeviate.wordpress.com/" target="_blank">
            Normal Deviate
           </a>
           中写下大号书评：
          </p>
          <h2>
           <a href="http://taoshistat.wordpress.com/2012/12/06/2100/" rel="bookmark" title="Permanent Link to Nate Silver is a Frequentist: Review of ``the signal and the noise''">
            Nate Silver is a Frequentist: Review of “the signal and the noise”
           </a>
          </h2>
          <blockquote>
           <p>
            ［……］As you can see, I liked the book very much and I highly recommend it.
           </p>
           <p>
            But …
           </p>
           <p>
            I have one complaint. Silver is a big fan of Bayesian inference, which is fine. Unfortunately, he falls into that category I referred to
            <a href="http://normaldeviate.wordpress.com/2012/11/17/what-is-bayesianfrequentist-inference/">
             a few posts ago.
            </a>
            He confuses “Bayesian inference” with “using Bayes’ theorem.” His description of frequentist inference is terrible. He seems to equate frequentist inference with Fisherian significance testing, most using Normal distributions. Either he learned statistics from a bad book or he hangs out with statisticians with a significant anti-frequentist bias.
           </p>
           <p>
            Have no doubt about it: Nate Silver is a frequentist. For example, he says:
           </p>
           <p>
            <strong>
             “One of the most important tests of a forecast — I would argue that it is the single most important one — is called calibration. Out of all the times you said there was a 40 percent chance of rain, how often did rain actually occur? If over the long run, it really did rain about 40 percent of the time, that means your forecasts were well calibrated.”
            </strong>
           </p>
           <p>
            It does not get much more frequentist than that. And if using Bayes’ theorem helps you achieve long run frequency calibration, great. If it didn’t, I have no doubt he would have used something else. But his goal is clearly to have
            <strong>
             good long run frequency behavior
            </strong>
            .［……］
           </p>
          </blockquote>
          <p>
           一时间风雨突起，这个关于 Frequentist or Bayesian 的争议话题又现江湖。第一个杀出来的是？没错！正是大侠
           <a href="http://andrewgelman.com/" rel="external nofollow">
            Andrew Gelman
           </a>
           (Department of Statistics, Columbia University)，著名的
           <a href="http://andrewgelman.com/" title="Statistical Modeling, Causal Inference, and Social Science: ">
            Statistical Modeling, Causal Inference, and Social Science
           </a>
           的博主。
          </p>
          <blockquote>
           <p>
            Larry:
           </p>
           <p>
            There is such a thing as Bayesian calibration of probability forecasts. If you are predicting a binary outcome y.new using a Bayesian prediction p.hat (where p.hat is the posterior expectation E(y.new|y), then Bayesian calibration requires that E(y.new|y.hat) = y.hat for any y.hat. This isn’t the whole story (as always, calibration matters but so does precision), but it’s not the same as frequentist calibration or unbiasedness. In frequentist calibration, the expectation is taken conditional on the value of the unknown parameters theta in the model. The calibration you describe above (for another example, see
            <a href="http://andrewgelman.com/2010/11/some_thoughts_o_8/" rel="nofollow">
             here
            </a>
            and scroll down) is unconditional on theta, thus Bayesian. So I disagree with you that those calibrations are frequentist and not Bayesian. But of course I completely agree with you that the concept of frequency performance of methods is important. It’s just that Bayesian calibration does not condition on theta.
           </p>
          </blockquote>
          <p>
           江湖不宁，争论又起，各路人马
           <a href="http://normaldeviate.wordpress.com/2012/12/04/nate-silver-is-a-frequentist-review-of-the-signal-and-the-noise/#comments" target="_blank">
            加入论战
           </a>
           。大侠
           <a href="http://xianblog.wordpress.com" target="_blank">
            XI’AN’ OG
           </a>
           也出面提出把这场论战记入江湖册：
          </p>
          <blockquote>
           <p>
            Would you mind publishing this review in
            <a href="http://chance.amstat.org" target="_blank">
             CHANCE
            </a>
            , by any chance???
           </p>
          </blockquote>
          <p>
           看大侠们挥舞这各项理论和哲学思想，小的不尽倒吸一口凉气。
          </p>
          <p>
           问题原来是神算子是否属于少林派，还是武当派。怎么忽然就变成各派根据其所著之书，来统计推断其个人取向了呢？然后有演变为了两派镇派宝典根基的争论了。
          </p>
          <p>
           要是实在关心神算子心仪那派的问题，不如找来神算子本人问一下，到底人家对哪里更有归属感，不就行了。实在找不到本人，就@他，tweet 一下好了。。。。。。
          </p>
          <p>
           走你！
          </p>
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            施涛
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          at 10:58
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          Tagged with:
          <a href="http://blog.cos.name/taoshi/tag/andrew-gelman/" rel="tag">
           Andrew Gelman
          </a>
          ,
          <a href="http://blog.cos.name/taoshi/tag/bayesian/" rel="tag">
           Bayesian
          </a>
          ,
          <a href="http://blog.cos.name/taoshi/tag/frequentist/" rel="tag">
           Frequentist
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          ,
          <a href="http://blog.cos.name/taoshi/tag/larry-wasserman/" rel="tag">
           Larry Wasserman
          </a>
          ,
          <a href="http://blog.cos.name/taoshi/tag/nate-silver/" rel="tag">
           Nate Silver
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          ,
          <a href="http://blog.cos.name/taoshi/tag/the-signal-and-the-noise/" rel="tag">
           The Signal and the Noise
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       <article class="full-content post-1847 post type-post status-publish format-standard hentry category-61 category-23 category-84 tag-181 tag-102 tag-101 category-61-id category-23-id category-84-id post-seq-2 post-parity-even meta-position-corners fix" id="post-1847">
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          <h2 class="posttitle">
           <a class="entry-title" href="http://blog.cos.name/taoshi/2012/11/26/%e7%be%a4%e4%bd%93%e7%9a%84%e6%99%ba%e6%85%a7/" rel="bookmark" title="群体的智慧">
            群体的智慧
           </a>
          </h2>
          <div class="postdata fix">
           <span class="category">
            <span class="icon">
            </span>
            <a href="http://blog.cos.name/taoshi/category/%e6%95%b0%e6%8d%ae%e5%88%86%e6%9e%90/" rel="category tag">
             数据分析
            </a>
            ,
            <a href="http://blog.cos.name/taoshi/category/%e6%95%b0%e6%8d%ae%e6%8c%96%e6%8e%98/" rel="category tag">
             数据挖掘
            </a>
            ,
            <a href="http://blog.cos.name/taoshi/category/%e7%bb%9f%e8%ae%a1/" rel="category tag">
             统计
            </a>
           </span>
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            </span>
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             7 Responses »
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         <div class="date">
          <span class="month">
           11月
          </span>
          <span class="day">
           26
          </span>
          <span class="year">
           2012
          </span>
         </div>
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        <span class="updated" title="2012-11-26T23:48:02+00:00">
        </span>
        <div class="entry-container fix">
         <div class="entry entry-content fix">
          <p>
           首先声明：这里的群体只在数据分析范畴，不要瞎联想到社会实践中。不慎应用，后果自负。在说任何之前，先推荐一本书：
           <a href="http://book.douban.com/subject/4924898/" target="_blank">
            群体的智慧
           </a>
          </p>
          <p>
           <img src="http://img3.douban.com/lpic/s4507474.jpg"/>
          </p>
          <p>
           我也不知道翻译的水平如何，如果读不下去可以看
           <a href="http://www.amazon.com/Wisdom-Crowds-James-Surowiecki/dp/0385721706" target="_blank">
            原版的
           </a>
           。
          </p>
          <p>
           早就在想传播一下这个有趣的话题，但它实在是太大，太沉重，不知在哪个范围内讨论比较好。
           <a href="http://book.douban.com/subject/4924898/" target="_blank">
            群体的智慧
           </a>
           一书的开头就把这个话题扩大到民主决策和精英决策的对比，实在出乎我的准备范围。
          </p>
          <p>
           刚好又
           <a href="http://www.loyhome.com/我（对于统计方法）的一些偏见/" target="_blank">
            被人点名
           </a>
           ，
          </p>
          <blockquote>
           <p>
            再再再比如，没有假设简单的那些机器学习模型中，我最最最最无法认同的就是最粗暴的把
            <a href="http://www.loyhome.com/r%e5%b9%b6%e8%a1%8c%e5%81%9a%e5%a4%a7%e6%95%b0%e6%8d%ae%e6%97%b6%e9%97%b4%e5%ba%8f%e5%88%97%e5%88%86%e6%9e%90%e4%b8%8ebootstrap/" title="R并行做大数据时间序列分析与bootstrap">
             各种模型结果混合起来
            </a>
            ，用类似bootstrap的方法求得置信区间之类…这简直是就毫无办法之下的粗暴猜测嘛。
           </p>
           <p>
            然后最后一个问题，施老师说，这个某种程度上反映了“群体智慧”。呃，好吧，就算每个模型都提取了一定的信息量，然后这么混合起来就是万灵药了？怎么听怎么像中药一锅煮的感觉，而不是西药那么配方分明…
           </p>
          </blockquote>
          <p>
           那我就在我知道的数据分析的框架内来汇报一下。 我觉得（个人意见，个人意见）数理统计作为数据分析的一部分，基本上就是在用平均的想法争取把误差减小，让有用信号自己站出来。不管是参数估计，假设检验，各类回归，各类预测，时间空间，黑箱白箱，黑猫白猫。。。但是怎么平均就体现了各种方法的区别。
          </p>
          <p>
           那就先举个最粗暴的中药一锅煮的例子：
           <a href="http://zh.wikipedia.org/wiki/随机森林" target="_blank">
            随机森林
           </a>
           （Random Forest），
           <a href="http://en.wikipedia.org/wiki/Leo_Breiman" target="_blank">
            Loe Breiman
           </a>
           的大作。在做分类（classification）时，每次从已有数据中
           <em>
            <strong>
             随机选取
            </strong>
           </em>
           （bootstrap 或随机抽) 一部分观测值和
           <em>
            <strong>
             随机抽出一小部分变量
            </strong>
           </em>
           。在这个小数据上建个小的分类树。
           <em>
            <strong>
             独立重复
            </strong>
           </em>
           上面一步得到一批小的分类树。等有新的观测值要被分类时，把TA扔进各个弱小的分类树来分别做决定，最后让这些小树来
           <em>
            <strong>
             投个票
            </strong>
           </em>
           就行了。这没有任何模型和技术含量的天马流行算法行吗？实践证明它还真行。
          </p>
          <p>
           说了半天，这和群体的智慧有关系吗？我当然也不同意“就算每个模型都提取了一定的信息量，然后这么混合起来就是万灵药了”。何时可以利用群体的智慧也是有条件的。前人和现代人经验总结了
           <a href="http://en.wikipedia.org/wiki/The_Wisdom_of_Crowds" target="_blank">
            四条
           </a>
           ：
          </p>
          <table>
           <tbody>
            <tr>
             <td>
              Diversity of
              <a href="http://en.wikipedia.org/wiki/Opinion" title="Opinion">
               opinion
              </a>
             </td>
             <td>
              Each person should have private information even if it’s just an eccentric interpretation of the known facts.
             </td>
            </tr>
            <tr>
             <td>
              Independence
             </td>
             <td>
              People’s opinions aren’t determined by the opinions of those around them.
             </td>
            </tr>
            <tr>
             <td>
              Decentralization
             </td>
             <td>
              People are able to specialize and draw on local knowledge.
             </td>
            </tr>
            <tr>
             <td>
              Aggregation
             </td>
             <td>
              Some mechanism exists for turning private judgments into a collective
              <a href="http://en.wikipedia.org/wiki/Decision_making" title="Decision making">
               decision
              </a>
              .
             </td>
            </tr>
           </tbody>
          </table>
          <p>
           回头看一下，
           <a href="http://zh.wikipedia.org/wiki/随机森林" target="_blank">
            随机森林
           </a>
           不正是在试图复制用随机抽取观测值和变量来产生Diversity of opnion，用独立随机抽取来使小树们有自己的见解（Independece），用小树而不是线性模型来提取局部信息（Decentralization），用一树一票来民主集中（Aggregation）吗？
          </p>
          <p>
           所以我认为这个看来最粗暴黑箱子其实还是很透明的，而且是经过精心合理设计。中药一锅煮应该不会很有效，但煮什么，怎么煮还是很有学问的。煮好了没准搞出了凉茶什么的百病通杀呢（placebo effect)。
          </p>
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            好的和不负责任的数据分析在《自然》杂志争议文章中的完全体现
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         <div class="date">
          <span class="month">
           8月
          </span>
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           07
          </span>
          <span class="year">
           2012
          </span>
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        <span class="updated" title="2012-08-07T00:27:10+00:00">
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         <div class="entry entry-content fix">
          <p>
           引起热议的《自然》杂志新闻文章
           <a href="http://www.nature.com/news/why-great-olympic-feats-raise-suspicions-1.11109" target="_blank">
            Why great Olympic feats raise suspicions
           </a>
           今天有了新进展。杂志的主编
           <strong>
            <em>
             Tim Appenzeller
            </em>
           </strong>
           <em>
            Chief Magazine Editor,
           </em>
           Nature 和
           <strong>
            <em>
             Philip Campbell
            </em>
           </strong>
           <em>
            Editor-in-Chief,
           </em>
           Nature 发了说明
           <a href="http://www.nature.com/news/why-great-olympic-feats-raise-suspicions-1.11109#/ed_note_continued" target="_blank">
            an editor’s note
           </a>
           并向读者和叶诗文道歉 (这是11:40am EST, August 6, 2012我看到的)
          </p>
          <blockquote>
           <h2>
            <strong>
             EDITORS’ NOTE (continued)
            </strong>
           </h2>
           <p>
            <em>
             The news story was triggered by a debate that was already active, concerning the scale of Ye Shiwen’s victory. Such debates have arisen over many outstanding feats in the past, by athletes from many countries, and it is wrong to suggest, as many of the critics do, that we singled her out because of her nationality.
            </em>
           </p>
           <p>
            <em>
             The story’s intention as an Explainer was to examine how science can help resolve debates over extraordinary performances, not to examine those performance statistics in detail. Several analyses done by others convinced us that it was fair to characterize Ye’s performance as ‘anomalous’ — in the sense that it was statistically unusual. But we acknowledge that the combination of errors discussed above and the absence of a more detailed discussion of the statistics (which with hindsight we regret) gave the impression that we were supporting accusations against her, even though this was emphatically not our intention. For that, we apologize to our readers and to Ye Shiwen.
            </em>
           </p>
           <p>
            <strong>
             <em>
              Tim Appenzeller
             </em>
            </strong>
            <em>
             Chief Magazine Editor,
            </em>
            Nature
            <br/>
            <strong>
             <em>
              Philip Campbell
             </em>
            </strong>
            <em>
             Editor-in-Chief,
            </em>
            Nature
           </p>
          </blockquote>
          <p>
           前两天我也对原文的统计分析
           <a href="http://blog.cos.name/taoshi/2012/08/02/nature-why-great-olympic-feats-raise-suspicions/" target="_blank">
            有质疑
           </a>
           ，连饶毅写了
           <a href="http://blog.sciencenet.cn/blog-2237-598917.html" target="_blank">
            致《自然》杂志总编的信
           </a>
           。看到
           <a href="http://www.nature.com/news/why-great-olympic-feats-raise-suspicions-1.11109#/Lai_Jiang" target="_blank">
            好的统计分析
           </a>
           把烂文章指点的体无完肤，还是挺有感触的。
          </p>
          <p>
           但是我还是对总编的中的一句话不解：
           <strong>
            “
            <em>
             Several analyses done by others convinced us that it was fair to characterize Ye’s performance as ‘anomalous’ — in the sense that it was statistically unusual.”
            </em>
           </strong>
          </p>
          <p>
           我希望这 “fair”是一个笔误, 但或许不是呢。如果主编被说服相信叶诗文的表现是离谱的，那主编们能不能指出是那个分析让你们相信叶诗文的表现不正常呢？我有15年以上在大学中学习，教授，和研究统计的经历，但我怎么从评论中看到的大多是指出叶诗文的表现没有不正常呢？
          </p>
          <p>
           希望你们这一次不再为没有包括详细的统计分析而后悔！
          </p>
          <p>
          </p>
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            Nature文章: 为何好的奥林匹克成绩引起怀疑
           </a>
          </h2>
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          <p>
           8/9/2012，更新：今天收到《自然》杂志自动生成邮件：
          </p>
          <p>
           The following post you wrote on the Nature News website has been hidden by the moderator in accordance with our terms and conditions.
          </p>
          <blockquote>
           <p>
            To editor Brian Owens:
            <br/>
            I wonder the so called ‘performance profiling’, as mentioned in the title of this article, could be used to judge if the editor was drunk on duty or is lack of basic knowledge of Statistics.
           </p>
           <p>
            If this is article used to highlight what so called science with crappy data analysis cannot tell us, congratulations! You passed with A+.
           </p>
          </blockquote>
          <p>
           This comment contains abusive language and as such breaches our Terms of Service.
          </p>
          <p>
           –
           <em>
            Nature News
           </em>
           editors
          </p>
          <p>
           －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
          </p>
          <p>
           本以为可以停下来对数字的兴趣来看几天奥运，但看了
           <a href="http://www.nature.com/nature/index.html" target="_blank">
            Nature杂志
           </a>
           的一篇文章， “
           <a href="http://www.nature.com/news/why-great-olympic-feats-raise-suspicions-1.11109" target="_blank">
            Why great Olympic feats raise suspicions, ‘Performance profiling’ could help to dispel doubts
           </a>
           “，后还是忍不住写点什么。
          </p>
          <p>
           看了文章马上让我想起这样的书目：
           <a href="http://www.amazon.com/Damned-Lies-Statistics-Untangling-Politicians/dp/0520219783/" target="_blank">
            Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists
           </a>
           and
           <a href="http://www.amazon.com/More-Damned-Lies-Statistics-Numbers/dp/0520238303/" target="_blank">
            More Damned Lies and Statistics: How Numbers Confuse Public Issues
           </a>
           .
          </p>
          <p>
           NAUTRE, 你叫人情何以堪？我现在还是不把你分类到新闻媒体之列，但或许你很快就证明我是错的。
          </p>
          <div class="wp-caption aligncenter" style="width: 410px">
           <img src="http://www.nature.com/polopoly_fs/7.5628.1343835371!/image/149445070%20reduced.jpg_gen/derivatives/landscape_400/149445070%20reduced.jpg"/>
           <p class="wp-caption-text">
            L. NEAL /AFP / GETTY IMAGES
           </p>
          </div>
          <blockquote>
           <p>
            <strong>
             Was Ye’s performance anomalous?
            </strong>
            <br/>
            Yes. Her time in the 400 IM was more than 7 seconds faster than her time in the same event at a major meet in July. But what really raised eyebrows was her showing in the last 50 metres, which she swam faster than US swimmer Ryan Lochte did when he won gold in the men’s 400 IM on Saturday, with the second-fastest time ever for that event.
           </p>
          </blockquote>
          <p>
           比较叶诗文和罗切特在400米混合泳的最后50米时间太误导。 这样的分析写新闻报道还可以，要鳌头吗！可稍微有点统计常识的人都不会只用这样简单的数字比较来支持严格的观点的。 有位读者
           <a href="http://www.nature.com/news/why-great-olympic-feats-raise-suspicions-1.11109#/comment-47487" target="_blank">
            Lai Jiang
           </a>
           评论的很到位：
          </p>
          <blockquote>
           <p>
            First, to compare a player’s performance increase, the author used Ye’s 400m IM time and her performance at the World championship 2011, which are 4:28.43 and 4:35.15 respectively, and reached the conclusion that she has got an “anomalous” increase by ~7 sec (6.72 sec). In fact she’s previous personal best was 4:33.79 at Asian Games 2010
            <sup>
             <a href="http://www.nature.com/news/why-great-olympic-feats-raise-suspicions-1.11109#fnad852dd0f9344e4c9394fd447fd36629">
              1
             </a>
            </sup>
            . This leads to a 5.38 sec increase. In a sport event that 0.1 sec can be the difference between the gold and silver medal, I see no reason that 5.38 sec can be treated as 7 sec. ……
           </p>
           <p>
            Third, to compare Ryan Lochte’s last 50m to Ye’s is a textbook example of what we call to cherry pick your data. Yes, Lochte is slower than Ye in the last 50m, but (as pointed out by Zhenxi) Lochte has a huge lead in the first 300m so that he chose to not push himself too hard to conserve energy for latter events (whether this conforms to the Olympic spirit and the “use one’s best efforts to win a match” requirement that the BWF has recently invoked to disqualify four badminton pairs is another topic worth discussing, probably not in Nature, though). On the contrary, Ye is trailing behind after the first 300m and relies on freestyle, which she has an edge, to win the game. Failing to mention this strategic difference, as well as the fact that Lochte is 23.25 sec faster (4:05.18) over all than Ye creates the illusion that a woman swam faster than the best man in the same sport, which sounds impossible. Put aside the gender argument, I believe this is still a leading question that implies the reader that something fishy is going on.
           </p>
           <p>
            Fourth, another example of cherry picking. In the same event there are four male swimmers that swam faster than both Lochter (29.10 sec)3 and Ye (28.93 sec)4: Hagino (28.52 sec), Phelps (28.44 sec), Horihata (27.87 sec) and Fraser-Holmes (28.35 sec). As it turns out if we are just talking about the last 50m in a 400m IM, Lochter would not have been the example to use if I were the author. What kind of scientific rigorousness that author is trying to demonstrate here? Is it logical that if Lochter is the champion, we should assume he leads in every split? That would be a terrible way to teach the public how science works.
           </p>
          </blockquote>
          <p>
           我是真心希望象Nature这样的顶尖杂志能认真些。或许Nature
           <a href="http://www.nature.com/news/why-great-olympic-feats-raise-suspicions-1.11109#/comment-47526" target="_blank">
            线上新闻主编的回答
           </a>
           可以解释：
          </p>
          <blockquote>
           <p>
            We appreciate that the case of Ye Shiwen is a sensitive one for some readers. However, I would like to point out that this story was not intended to insinuate that Ye is guilty of anything. As we point out in the first paragraph, she has never failed a drug test and so is the rightful Olympic champion.
           </p>
           <p>
            We wanted to use the controversy as a way to highlight what science can and can’t tell us with respect to athletes’ performance. We have done similar stories before, for example in the case of South African runner
            <a href="http://www.nature.com/news/2009/090820/full/news.2009.850.html">
             Caster Semenya
            </a>
           </p>
           <p>
            Congratulations to Ye Shiwen on her incredible win!
           </p>
           <p>
            Brian Owens
            <br/>
            Online news editor
           </p>
          </blockquote>
          <p>
           我怀疑文章标题中的’performance profiling’ 方法是否可以用来猜测主编是在审这稿时喝醉了呢，还是缺乏基本的统计知识。如果这文章是象主编所说的用来展示什么是用糊涂数据分析支持的科学不能发现的，恭喜你！你的表现太好了。
          </p>
          <p>
           归根结底，数字只是数字，但每个数字后面都有它的故事。别只看到数字的表面标价（¥6 或 $1）!
          </p>
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           游泳
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           自然杂志
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            John and David
           </a>
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            ,
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            </a>
            ,
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             统计咨询
            </a>
            ,
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             职业介绍
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          <p>
           接着上回
           <a href="http://blog.cos.name/taoshi/?p=1674" rel="bookmark" target="_blank" title="测谎仪与黄金套索">
            测谎仪与黄金套索
           </a>
           讲另一个
           <a href="http://www.stat.cmu.edu/~fienberg/" target="_blank">
            Stephen E. Fienberg
           </a>
           五月份在
           <a href="http://www.stat.osu.edu/" target="_blank">
            系里
           </a>
           的
           <a href="http://www.stat.osu.edu/event/cl-and-md-rustagi-memorial-lecture-statistics-service-nation" target="_blank">
            C.L. and M.D. Rustagi Memorial Lecture
           </a>
           中给的“统计服务社会”的报告中提到的故事 （喜欢读英文的可以
           <a href="http://wp.me/p1OR7u-qD" target="_blank">
            看这里
           </a>
           ）。
          </p>
          <p>
           报告从一个问题开始：”谁在实际应用中最先使用贝叶斯层次模型?” (温馨提示：不是
           <a href="http://www.stat.duke.edu/~berger/" target="_blank">
            Jim berger
           </a>
           🙂 )
          </p>
          <p>
           答案就在下面的老照片里：
           <strong>
            <a href="http://www.stat.berkeley.edu/~brill/" target="_blank">
             David Brillinger
            </a>
           </strong>
           (左下) 和
           <strong>
            <a href="http://en.wikipedia.org/wiki/John_Tukey" target="_blank">
             John Tukey
            </a>
           </strong>
           (右下， 6月16日, 1915 – 7月 26日, 2000). 今天刚好是John逝世12周年。照片是他们在60年代为美国全国广播公司做美国总统选举预测时拍的。
          </p>
          <p style="text-align: center">
           <a href="http://i.imgur.com/4C6ec.jpg">
            <img src="http://i.imgur.com/4C6ec.jpg"/>
           </a>
          </p>
          <p>
           等等! 我和David的办公室邻居了四年，怎么就从没从他嘴里提起过贝叶斯层次模型呢？
          </p>
          <p>
           出于好奇，我找到了David写的关于John的一片纪念文章,
           <a href="http://www.stat.berkeley.edu/~brill/Papers/life.pdf" target="_blank">
            JOHN W. TUKEY: HIS LIFE AND PROFESSIONAL CONTRIBUTIONS
           </a>
           (
           <em>
            The Annals of Statistics 2002, Vol. 30, No. 6, 1535-1575
           </em>
           ), 里面对选举预测是这样描述的:
          </p>
          <blockquote>
           <div>
            Starting with the 1962 Congressional election John assembled a statistical team to develop the required methodology and to analyze the results as they flowed in on election night. Early members of the team included Bob Abelson, Dick Link, John Mauchly, David Wallace, and myself.
           </div>
           <div>
           </div>
           <div>
           </div>
          </blockquote>
          <div>
           文章挺长，但是非常有趣和有料。通过各种小事，让我们看到了John Tukey 的一生和他对统计的推进和贡献。摘录几个小片段如下：
          </div>
          <div>
          </div>
          <div>
          </div>
          <blockquote>
           <div>
            <ul>
             <li>
              <strong>
               Statistics is a science in my opinion, and it is no more a branch of mathematics than are physics, chemistry and economics; for if its methods fail the test of experience—not the test of logic—they are discarded
              </strong>
              . [TUKEY,J.W.(1953).The growth of experimental design in a research laboratory. InResearch Operations in Industry 303–313. King’s Crown Press, New York.]
             </li>
            </ul>
           </div>
           <ul>
            <li>
             One Christmas Tukey gave his students books of crossword puzzles as presents. Upon examining the books the students found that Tukey had removed the puzzle answers and had replaced them with words of the sense:
             <strong>
              Doing statistics is like doing crosswords except that one cannot know for sure whether one has found the solution.
             </strong>
            </li>
           </ul>
           <ul>
            <li>
             <strong>
              . . . the first time I was in a statistics course, I was there to teach it.
             </strong>
             [TUKEY,J.W.(1984). Speech when receiving James Madison Medal, Princeton Univ.]
            </li>
           </ul>
           <ul>
            <li>
             <strong>
              A consultant is a man who thinks with other people’s brains.
             </strong>
             [TUKEY,J.W.(1967).What can mathematicians do for the Federal Government? Amer. Math. Monthly 74 (1, Part II) 101–109. ]
            </li>
           </ul>
           <ul>
            <li>
             When on sabbatical in New Zealand 25 years ago this writer learned the following method to go between the centigrade and Fahrenheit scales of temperature in a couple of important cases—one simply reverses the digits of 61 and 16 and of 82 and 28. I told this to John and he very quickly came up with another case. He remarked that 40 converts to 04.
            </li>
           </ul>
          </blockquote>
          <div>
           <p>
            别忘了读一下
            <a href="http://www.stat.berkeley.edu/~brill/Papers/life.pdf" target="_blank">
             全文
            </a>
            和浏览一下
            <a href="http://www.stat.berkeley.edu/~brill/Papers/life.pdf" target="_blank">
             附录E
            </a>
            , 你一定不会失望的。
           </p>
           <p>
            谢谢你，David!  谢谢你， John!
           </p>
          </div>
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             数据分析
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            ,
            <a href="http://blog.cos.name/taoshi/category/%e7%bb%9f%e8%ae%a1%e5%ba%94%e7%94%a8/" rel="category tag">
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           16
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           2012
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        <div class="entry-container fix">
         <div class="entry entry-content fix">
          <p>
           <a href="http://www.stat.cmu.edu/~fienberg/" target="_blank">
            Stephen E. Fienberg
           </a>
           教授五月份在
           <a href="http://www.stat.osu.edu" target="_blank">
            系里
           </a>
           的
           <a href="http://www.stat.osu.edu/event/cl-and-md-rustagi-memorial-lecture-statistics-service-nation" target="_blank">
            C.L. and M.D. Rustagi Memorial Lecture
           </a>
           中给了个 Statistics in Service to the Nation 的报告。那时就想把其中一些有趣的话题记下来，直到今天才用空查了些相关资料。那就从报告最后提到的测谎仪和
           <a href="http://zh.wikipedia.org/wiki/李文和" target="_blank">
            李文和
           </a>
           （
           <a href="http://en.wikipedia.org/wiki/Wen_Ho_Lee" target="_blank">
            Wen Ho Lee
           </a>
           )事件讲起。
          </p>
          <blockquote>
           <p>
            李文和（Wen Ho Lee，1939年12月21日－），生于
            <a href="http://zh.wikipedia.org/wiki/%E8%87%BA%E7%81%A3" title="臺灣">
             臺灣
            </a>
            <a href="http://zh.wikipedia.org/wiki/%E5%8D%97%E6%8A%95" title="南投">
             南投
            </a>
            ，
            <a href="http://zh.wikipedia.org/wiki/%E5%9C%8B%E7%AB%8B%E6%88%90%E5%8A%9F%E5%A4%A7%E5%AD%B8" title="國立成功大學">
             國立成功大學
            </a>
            機械工程學系
            <a href="http://zh.wikipedia.org/wiki/%E5%AD%B8%E5%A3%AB" title="學士">
             學士
            </a>
            ，
            <a href="http://zh.wikipedia.org/wiki/%E5%BE%B7%E5%85%8B%E8%90%A8%E6%96%AF%E5%86%9C%E5%B7%A5%E5%A4%A7%E5%AD%A6" title="德克萨斯农工大学">
             德克薩斯農工大學
            </a>
            （Texas A&amp;M University）博士，於
            <a href="http://zh.wikipedia.org/wiki/1974%E5%B9%B4" title="1974年">
             1974年
            </a>
            歸化為美國
            <a href="http://zh.wikipedia.org/wiki/%E5%85%AC%E6%B0%91" title="公民">
             公民
            </a>
            。他曾在
            <a href="http://zh.wikipedia.org/wiki/%E7%BE%8E%E5%9C%8B" title="美國">
             美國
            </a>
            <a href="http://zh.wikipedia.org/wiki/%E6%B4%9B%E6%96%AF%E9%98%BF%E6%8B%89%E8%8E%AB%E6%96%AF%E5%9C%8B%E5%AE%B6%E5%AF%A6%E9%A9%97%E5%AE%A4" title="洛斯阿拉莫斯國家實驗室">
             洛斯阿拉莫斯國家實驗室
            </a>
            爲
            <a href="http://zh.wikipedia.org/wiki/%E5%8A%A0%E5%B7%9E%E5%A4%A7%E5%AD%B8" title="加州大學">
             加州大學
            </a>
            工作。他于
            <a href="http://zh.wikipedia.org/wiki/1999%E5%B9%B4" title="1999年">
             1999年
            </a>
            被指控爲
            <a href="http://zh.wikipedia.org/wiki/%E4%B8%AD%E8%8F%AF%E4%BA%BA%E6%B0%91%E5%85%B1%E5%92%8C%E5%9C%8B" title="中華人民共和國">
             中華人民共和國
            </a>
            竊取了關於美國
            <a href="http://zh.wikipedia.org/wiki/%E6%A0%B8%E6%AD%A6%E5%99%A8" title="核武器">
             核武庫
            </a>
            的機密。在調查員收回這些最初的指控之後，政府進行了一輪新的調查並以不正當處理內部資料的罪名控告李文和。
            <a href="http://zh.wikipedia.org/wiki/2000%E5%B9%B4" title="2000年">
             2000年
            </a>
            ，李與
            <a href="http://zh.wikipedia.org/wiki/%E7%BE%8E%E5%9C%8B%E8%81%AF%E9%82%A6%E6%94%BF%E5%BA%9C" title="美國聯邦政府">
             美國聯邦政府
            </a>
            達成訴訟協議：他對一項罪名認罪，政府收回其他58項指控並將其釋放。（
            <a href="http://zh.wikipedia.org/wiki/李文和" target="_blank">
             维基百科
            </a>
            ）
           </p>
          </blockquote>
          <p>
           1998年12月23日，李文和被安排测谎并被告知通过测谎仪检验，但是却被收回Q级cleariance. 在美国国会的询问下，美国能源部请国家研究理事会(
           <a href="http://nationalacademies.org/nrc/" target="_blank">
            National Research Council
           </a>
           , NRC）对测谎仪（polygraph）的准确性做全面研究。国家研究理事会组成了专门委员会来展开研究，
           <a href="http://www.stat.cmu.edu/~fienberg/" target="_blank">
            Stephen E. Fienberg
           </a>
           当时就是这个委员会的主席。
          </p>
          <p>
           委员会对于在2002年10月公布了
           <a href="http://www.nap.edu/catalog.php?record_id=10420" target="_blank">
            报告结果
           </a>
           。报告中用了非常规的统计方法总结了历史上曾经对测谎仪的进行的测试。对于一个仪器的准确度的衡量可以用
           <a href="http://en.wikipedia.org/wiki/Receiver_operating_characteristic" target="_blank">
            ROC cruve
           </a>
           . 但如何把多个研究结果中的ROC cruves 结合在一起分析呢？一维数据还好总结，可当数据是一些 ROC curves时怎么办呢？ 委员会对选择用 ROC cruve 下的面积（Area Under the Cruve）把这些曲线排序（下图中每个有符号连接曲线对应一个历史上的研究）。图中的两条实线对应AUC为0.81和0.91（0.25和0.75分位数）的两条人为划的线，他们之间刚好包含了50％的数据。用这些数据分析结果（更详细的在报告中），委员会建议历史上对测谎仪的准确度的研究并不能对测谎仪的准确性提供说服性的支持，建议减少测谎仪在使用。
          </p>
          <p>
           <a href="http://www.stat.cmu.edu/%7Efienberg/MagicLasso-StatSci-2005.pdf">
            <img src="http://i.imgur.com/iSqyl.jpg"/>
           </a>
          </p>
          <p>
           2003年9月4日，国会听证会上能源部副部长Kyle McSlarrow和Stephen E. Fienberg教授同时在国会作证。在Stephen后来的统计文章，
           <a href="http://www.stat.cmu.edu/%7Efienberg/MagicLasso-StatSci-2005.pdf" target="_blank">
            In Search of the Magic Lasso: The Truth About the Polygraph
           </a>
           by
           <em>
            Stephen E. Fienberg and Paul C. Stern
           </em>
           (Statistical Science, 2005, Vol. 20, No. 3, 249–260)，中，对听证会的有趣细节有详细描述。文章最后的结论很有启发：
          </p>
          <blockquote>
           <p>
            Our report had had a real impact on public policy, although not as big an impact as we might have liked! And clearly, the thought and ef- fort that had gone into the presentation of the data and the results, and in particular into the two tables, had paid. This was not a case of “how to lie with statistics,” but the reverse. It was a triumph for careful statistical analysis and presentation, telling the truth about what we know about attempts to detect lying.
           </p>
          </blockquote>
          <div class="wp-caption alignright" style="width: 130px">
           <a href="http://upload.wikimedia.org/wikipedia/en/5/58/WonderWomanV5.jpg">
            <img src="http://upload.wikimedia.org/wikipedia/en/5/58/WonderWomanV5.jpg"/>
           </a>
           <p class="wp-caption-text">
            Wonder Woman with Golden Lasso
           </p>
          </div>
          <p>
          </p>
          <p>
           另外还从文章中学了点可以告诉家里小人的知识：
          </p>
          <p>
           在试验和法律实践中用血压变化纪录来分析是否欺骗的想法可以追诉到
           <a href="http://en.wikipedia.org/wiki/William_Moulton_Marston" target="_blank">
            William Moulton Marston
           </a>
           在哈佛大学做研究生时（1915 to 1921）的工作。
          </p>
          <p>
           后来他最出名的是1940年出版了第一个以女性为主角的漫画书：
           <a href="http://en.wikipedia.org/wiki/Wonder_Woman" target="_blank">
            Wonder Woman
           </a>
           。最近给小人讲故事时，Wonder Woman经常晃着她的黄金套索 (Golden Lasso)闲逛找坏人, 套上谁TA就会说真话。
          </p>
          <p>
           看来也是用漫画对未完的研究给个希望的寄托吧。
          </p>
         </div>
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           <a class="entry-title" href="http://blog.cos.name/taoshi/2012/07/08/%e5%8d%9a%e8%b0%88%e7%bb%9f%e8%ae%a1%e5%ba%94%e7%94%a8/" rel="bookmark" title="博谈统计应用">
            博谈统计应用
           </a>
          </h2>
          <div class="postdata fix">
           <span class="category">
            <span class="icon">
            </span>
            <a href="http://blog.cos.name/taoshi/category/%e5%aa%92%e4%bd%93%e6%8a%a5%e9%81%93/" rel="category tag">
             媒体报道
            </a>
            ,
            <a href="http://blog.cos.name/taoshi/category/%e6%95%b0%e6%8d%ae%e5%88%86%e6%9e%90/" rel="category tag">
             数据分析
            </a>
            ,
            <a href="http://blog.cos.name/taoshi/category/%e7%bb%9f%e8%ae%a1%e5%ba%94%e7%94%a8/" rel="category tag">
             统计应用
            </a>
           </span>
           <span class="comments">
            <span class="icon">
            </span>
            <a href="http://blog.cos.name/taoshi/2012/07/08/%e5%8d%9a%e8%b0%88%e7%bb%9f%e8%ae%a1%e5%ba%94%e7%94%a8/#comments">
             1 Response »
            </a>
           </span>
          </div>
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         <div class="date">
          <span class="month">
           7月
          </span>
          <span class="day">
           08
          </span>
          <span class="year">
           2012
          </span>
         </div>
        </header>
        <!-- /.title-container -->
        <span class="post-format-icon">
        </span>
        <span class="updated" title="2012-07-08T19:06:14+00:00">
        </span>
        <div class="entry-container fix">
         <div class="entry entry-content fix">
          <p>
           终于找到了上月在西安和西北大学低年级同学交流时的幻灯片[
           <a href="http://www.stat.osu.edu/~taoshi/博谈统计应用.pdf" target="_blank">
            pdf
           </a>
           ]，分享一下。
          </p>
          <p>
           摘要广告如下：
           <br/>
           <img src="http://i.imgur.com/9fNCe.jpg"/>
           <br/>
           <img src="http://i.imgur.com/JEN5i.jpg"/>
           <br/>
           <img src="http://i.imgur.com/0HAT8.jpg"/>
           <br/>
           <img src="http://i.imgur.com/yI9Lx.jpg"/>
           <br/>
           <img src="http://i.imgur.com/32lz4.jpg"/>
           <br/>
           <img src="http://i.imgur.com/VVCob.jpg"/>
           <br/>
           <img src="http://i.imgur.com/MzYJ7.jpg"/>
           <br/>
           <img src="http://i.imgur.com/vBN6O.jpg"/>
          </p>
          <hr/>
         </div>
         <!--entry -->
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          at 19:06
         </span>
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          Tagged with:
          <a href="http://blog.cos.name/taoshi/tag/%e7%bb%9f%e8%ae%a1%e5%ba%94%e7%94%a8/" rel="tag">
           统计应用
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       <article class="full-content post-1594 post type-post status-publish format-standard hentry category-63 category-61 category-62 tag-60 tag-boosting tag-58 tag-59 tag-64 category-63-id category-61-id category-62-id post-seq-8 post-parity-even meta-position-corners fix" id="post-1594">
        <header class="post-header title-container fix">
         <div class="title">
          <h2 class="posttitle">
           <a class="entry-title" href="http://blog.cos.name/taoshi/2012/07/06/%e5%b8%8c%e6%a0%bc%e6%96%af%e6%b3%a2%e8%89%b2%e5%ad%90/" rel="bookmark" title="希格斯玻色子与5σ">
            希格斯玻色子与5σ
           </a>
          </h2>
          <div class="postdata fix">
           <span class="category">
            <span class="icon">
            </span>
            <a href="http://blog.cos.name/taoshi/category/%e5%aa%92%e4%bd%93%e6%8a%a5%e9%81%93/" rel="category tag">
             媒体报道
            </a>
            ,
            <a href="http://blog.cos.name/taoshi/category/%e6%95%b0%e6%8d%ae%e5%88%86%e6%9e%90/" rel="category tag">
             数据分析
            </a>
            ,
            <a href="http://blog.cos.name/taoshi/category/%e7%a7%91%e5%ad%a6/" rel="category tag">
             科学
            </a>
           </span>
           <span class="comments">
            <span class="icon">
            </span>
            <a href="http://blog.cos.name/taoshi/2012/07/06/%e5%b8%8c%e6%a0%bc%e6%96%af%e6%b3%a2%e8%89%b2%e5%ad%90/#comments">
             7 Responses »
            </a>
           </span>
          </div>
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         </div>
         <!-- /.title -->
         <div class="date">
          <span class="month">
           7月
          </span>
          <span class="day">
           06
          </span>
          <span class="year">
           2012
          </span>
         </div>
        </header>
        <!-- /.title-container -->
        <span class="post-format-icon">
        </span>
        <span class="updated" title="2012-07-06T13:04:09+00:00">
        </span>
        <div class="entry-container fix">
         <div class="entry entry-content fix">
          <p>
           <strong>
            [更新，2012年7月14日]
           </strong>
           ：推荐对数据分析有兴趣的听一下这神粒子的声音（
           <a href="http://lhcsound.hep.ucl.ac.uk/page_sounds_higgs/Higgs.html" target="_blank">
            Listen to the decay of a god particle
           </a>
           ）。一群粒子物理学家，编曲家，软件工程师，和艺术家
           <a href="http://lhcsound.hep.ucl.ac.uk/page_about/About.html" target="_blank">
            用粒子对撞机的数据编成的曲目
           </a>
           。另类的数据展示！太强大了。
          </p>
          <p>
           2012年7月4日，欧洲核子研究组织（CERN， the
           <a href="http://public.web.cern.ch/public/en/About/Name-en.html" title="more about the CERN name">
            European Organization for Nuclear Research
           </a>
           ）的
           <a href="http://www.huanqiukexue.com/html/newqqkj/newwl/2012/0704/22320.html" target="_blank">
            物理学家们宣布
           </a>
           发现在欧洲大型强子对撞机中一种疑似
           <a href="http://zh.wikipedia.org/wiki/希格斯玻色子" target="_blank">
            希格斯玻色子
           </a>
           （
           <a href="http://en.wikipedia.org/wiki/Higgs_boson" target="_blank">
            Higgs Boson
           </a>
           ）。
          </p>
          <blockquote>
           <p>
            ［抄自wikipedia］：希格斯玻色子是
            <a href="http://zh.wikipedia.org/wiki/%E7%B2%92%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%B8" title="粒子物理學">
             粒子物理學
            </a>
            的
            <a href="http://zh.wikipedia.org/wiki/標準模型">
             标准模型
            </a>
            所预言的一种
            <a href="http://zh.wikipedia.org/wiki/%E5%9F%BA%E6%9C%AC%E7%B2%92%E5%AD%90" title="基本粒子">
             基本粒子
            </a>
            。
            <a href="http://zh.wikipedia.org/wiki/標準模型">
             标准模型
            </a>
            预言了62种基本粒子，希格斯玻色子是最后一种有待被实验证实的粒子。在希格斯玻色子是以物理学者
            <a href="http://zh.wikipedia.org/wiki/%E5%BD%BC%E5%BE%97%C2%B7%E5%B8%8C%E6%A0%BC%E6%96%AF" title="彼得·希格斯">
             彼得·希格斯
            </a>
            命名。由于它对于基本粒子的基础性质扮演极为重要的角色，因此在大众传媒中又被称为「上帝粒子」。
           </p>
          </blockquote>
          <p>
           近50年来，物理学家们一直在追寻希格斯玻色子，因为它的发现将使粒子物理的标准模型得到完善。下面的小片子通俗地讲了一下什么是希格斯玻色子。
          </p>
          <p>
           <object align="middle" classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" height="400" width="480">
            <param name="src" value="http://player.youku.com/player.php/sid/XNDIzNDExMTUy/v.swf">
            </param>
            <param name="allowfullscreen" value="true">
            </param>
            <param name="quality" value="high">
            </param>
            <param name="allowscriptaccess" value="always">
            </param>
            <embed align="middle" allowfullscreen="true" allowscriptaccess="always" height="400" quality="high" src="http://player.youku.com/player.php/sid/XNDIzNDExMTUy/v.swf" type="application/x-shockwave-flash" width="480">
            </embed>
           </object>
          </p>
          <p>
           作为只有高中物理水平的民科，我也能从物理学家们在宣布这发现时的激动（看下面视频）中感到这发现的重大。
          </p>
          <p>
           <object align="middle" classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" height="400" width="480">
            <param name="src" value="http://player.youku.com/player.php/sid/XNDIzNjIwOTY4/v.swf">
            </param>
            <param name="allowfullscreen" value="true">
            </param>
            <param name="quality" value="high">
            </param>
            <param name="allowscriptaccess" value="always">
            </param>
            <embed align="middle" allowfullscreen="true" allowscriptaccess="always" height="400" quality="high" src="http://player.youku.com/player.php/sid/XNDIzNjIwOTY4/v.swf" type="application/x-shockwave-flash" width="480">
            </embed>
           </object>
          </p>
          <p>
           除了表达对科学家的敬仰外，我也对其中提到的 5σ 很感兴趣。既然祖师爷
           <a href="http://en.wikipedia.org/wiki/John_Tukey" target="_blank">
            John Tukey
           </a>
           说过
          </p>
          <blockquote>
           <p>
            The
            <em>
             best
            </em>
            thing about being a
            <em>
             statistician
            </em>
            is that you get to play in everyone’s backyard，
           </p>
          </blockquote>
          <p>
           我倍受鼓励的来看看这 5σ 到底是怎么回事。视频中的点睛之笔：
          </p>
          <blockquote>
           <p>
            <em>
             We have observed a new boson with a mass of 125.3 +- 0.6 GeV at 4.9 σ significance.
            </em>
           </p>
          </blockquote>
          <p>
           念玩后大家鼓掌拥抱，热泪盈眶。一番周折后，我才终于找到了CERN的
           <strong>
            <a href="https://cdsweb.cern.ch/record/1459565" target="_blank">
             原版视频
            </a>
           </strong>
           （将近两小时，值得看看）。
          </p>
          <p>
           开始时只是想搞清楚这 5σ 怎么回事（35：10,第84页），没想到听到一堆统计词汇“multivariate analysis technique”，“p-value”,”sensitivity”, 等等劈头盖脸的飞来。最给力的是 Rolf Heuer 讲了一些用
           <a href="http://en.wikipedia.org/wiki/Boosting" target="_blank">
            Boosted decision tree
           </a>
           来提高分类器准确性的过程（18：20,第33页）。不出所料，研究中用到了很前沿的数据分析方法。老祖师果然没错。看来欲知其中细节，得看数据分析啊！
          </p>
          <p>
           比较遗憾的是我比较看不懂的是
           <a href="http://www.huanqiukexue.com/html/newqqkj/newwl/2012/0704/22320.html" target="_blank">
            环球科学
           </a>
           <a href="http://www.huanqiukexue.com/html/newqqkj/newwl/2012/0704/22320.html" target="_blank">
            （
           </a>
           <a href="http://www.huanqiukexue.com/html/newqqkj/newwl/2012/0704/22320.html" target="_blank">
            科
           </a>
           <a href="http://www.huanqiukexue.com/html/newqqkj/newwl/2012/0704/22320.html" target="_blank">
            学美国人中文版）的文章
           </a>
           “希格斯粒子现身LHC？”最后对 5σ 的解释：
          </p>
          <blockquote>
           <p>
            估计总体参数落在某一区间内，可能犯错误的概率为显著性水平，用α表示。1-α 为置信度或置信水平，其表明了区间估计的可靠性。显著性水平不是一个固定不变的数字，其越大，则原假设被拒绝的可能性愈大，文章中置信度为5σ（5个标准误差），说明原假设的可信程度达到了99.99997%
           </p>
          </blockquote>
          <p>
           好像这是把假设检验和置信区间绞在一起解释了。本来看了视频还我还觉着我这物理外行也看懂了，现在又被解释糊涂了。谁能看懂给解释一下？
          </p>
          <p>
          </p>
         </div>
         <!--entry -->
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        <footer class="post-footer postdata fix">
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          Posted by
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            施涛
           </a>
          </span>
          at 13:04
         </span>
         <span class="tags tax">
          <span class="icon">
          </span>
          Tagged with:
          <a href="http://blog.cos.name/taoshi/tag/5%cf%83/" rel="tag">
           5σ
          </a>
          ,
          <a href="http://blog.cos.name/taoshi/tag/boosting/" rel="tag">
           Boosting
          </a>
          ,
          <a href="http://blog.cos.name/taoshi/tag/%e5%b8%8c%e6%a0%bc%e6%96%af%e7%8e%bb%e8%89%b2%e5%ad%90/" rel="tag">
           希格斯玻色子
          </a>
          ,
          <a href="http://blog.cos.name/taoshi/tag/%e6%ac%a7%e6%b4%b2%e5%a4%a7%e5%9e%8b%e5%bc%ba%e5%ad%90%e5%af%b9%e6%92%9e%e6%9c%ba/" rel="tag">
           欧洲大型强子对撞机
          </a>
          ,
          <a href="http://blog.cos.name/taoshi/tag/%e7%bd%ae%e4%bf%a1%e5%8c%ba%e9%97%b4/" rel="tag">
           置信区间
          </a>
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        <header class="post-header title-container fix">
         <div class="title">
          <h2 class="posttitle">
           <a class="entry-title" href="http://blog.cos.name/taoshi/2012/05/07/prob_stat/" rel="bookmark" title="概率问题的统计解答">
            概率问题的统计解答
           </a>
          </h2>
          <div class="postdata fix">
           <span class="category">
            <span class="icon">
            </span>
            <a href="http://blog.cos.name/taoshi/category/%e6%95%b0%e6%8d%ae%e5%88%86%e6%9e%90/" rel="category tag">
             数据分析
            </a>
            ,
            <a href="http://blog.cos.name/taoshi/category/%e7%bb%9f%e8%ae%a1/" rel="category tag">
             统计
            </a>
            ,
            <a href="http://blog.cos.name/taoshi/category/%e7%bb%9f%e8%ae%a1%e5%ba%94%e7%94%a8/" rel="category tag">
             统计应用
            </a>
            ,
            <a href="http://blog.cos.name/taoshi/category/%e9%97%b2%e6%89%af/" rel="category tag">
             闲扯
            </a>
           </span>
           <span class="comments">
            <span class="icon">
            </span>
            <a href="http://blog.cos.name/taoshi/2012/05/07/prob_stat/#respond">
             No Responses »
            </a>
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         <div class="date">
          <span class="month">
           5月
          </span>
          <span class="day">
           07
          </span>
          <span class="year">
           2012
          </span>
         </div>
        </header>
        <!-- /.title-container -->
        <span class="post-format-icon">
        </span>
        <span class="updated" title="2012-05-07T22:34:25+00:00">
        </span>
        <div class="entry-container fix">
         <div class="entry entry-content fix">
          <p>
           看到
           <a href="http://www.weibo.com/1686830902/xz4i56oWn" target="_blank">
            一条新浪微薄
           </a>
           ：
          </p>
          <blockquote>
           <p>
            张栋_机器学习:【是女儿的概率？】一会吃午饭的时候, 我和一起吃饭的团队讨论这三道好玩的题 🙂 一对夫妻有2个孩子，给他家打电话（1）接电话的是女儿，请问另外一个孩子也是女儿的概率（2）接电话的是大女儿，请问另外一个孩子也是女儿的概率（3）接电话的是大女儿，请问这对夫妻若再生一个，也是女儿的概率？
           </p>
          </blockquote>
          <p>
           看评论挺有意思的。大家答案中大概包括这几种：0,   1／3, 1／2,  2／3,  1。 有抓住独立不独立，有讲条件概率或边缘分布的，还有根据问题中语言表达的。
          </p>
          <p>
           我也来凑个热闹。我的答案是“It depends”（放之四海节准的答案，呵呵）。我认为以上的答案都不太靠谱，因为这个和儿女的年龄有关系。
          </p>
          <p>
           为神马说以上答案不太对呢？主要是用数据说话，而不是靠直觉做假设。实际情况是：婴儿出生男女比例不是1：1。也就是说： 女婴出生率不是50％。
           <a href="http://www.stats.gov.cn/tjfx/jdfx/t20120118_402779722.htm" target="_blank">
            中国国家统计局公布的情况
           </a>
           ：
          </p>
          <blockquote>
           <p>
            2011年我国出生人口性别比为117.78，比上年下降0.16，出生人口性别比自2008年以来连续三年出现下降，表明出生人口性别比治理显现成效。
           </p>
          </blockquote>
          <p style="text-align: center;">
           <img src="http://www.stats.gov.cn/tjfx/jdfx/W020120118359882268582.gif"/>
          </p>
          <p style="text-align: center;">
           （注：出生人口性别比是每100名女婴对应男婴个数）
          </p>
          <p>
           难道这男多女少的出生比例也解释了在中国的相亲节目（非诚勿扰？）中男生要站在中间被了解的格局？也不尽然。这图显示的是婴儿出生比例，到了成年以后这比例变化太大了。同年龄组性别比例随年龄段增长而降低。中国的年龄分组数据在网上不好找，大家可以看一下
           <a href="http://www.census.gov/prod/cen2010/briefs/c2010br-03.pdf" target="_blank">
            美国2010人口普查的报告
           </a>
           。
          </p>
          <p>
           <a href="http://i.imgur.com/WXwAe.jpg">
            <img src="http://i.imgur.com/WXwAe.jpg"/>
           </a>
           <a href="https://taoshistat.files.wordpress.com/2012/05/fig_2010_2000.jpg">
            <br/>
           </a>
          </p>
          <p>
           前些天还就此写了个关于“
           <a href="http://taoshistat.wordpress.com/2012/01/27/men-die-earlier-or-women-live-longer/" target="_blank">
            Men die earlier or women live longer?
           </a>
           ”的小评论。 出生比例的差别，男女在各年龄段的死亡比例的差别，和各年龄段移民中男女比例的差别一起可以解释上面这个图中的结果。
          </p>
          <p>
           言归正传，根据这样的数据，上面的题目的答案应该这女儿的年龄很有关系。当然会有概率专家讲了：我们可以通过积分把年龄因素去掉，那就把这留做一道考试题吧 。。。结果好像不影响我的结论：“1／2,  1／3,  2／3,  1 这些都不靠谱”。
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            Learning applied statistics from David Freedman
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           11月
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           07
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           2011
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          <p>
           <a href="http://blog.cos.name/taoshi/files/2011/11/book.jpg">
            <img src="http://blog.cos.name/taoshi/files/2011/11/book.jpg?w=175"/>
           </a>
           Just suit up for the first time since the job interview season of Winter 2005. As one of those who got promoted this year, I attended the
           <a href="http://library.osu.edu/blogs/librarynews/2011/10/27/faculty-recognition-program-november-7/" target="_blank">
            Faculty Recognition Program
           </a>
           today and got a chance to look closely at the book, “
           <a href="http://www.amazon.com/Statistical-Models-Practice-David-Freedman/dp/0521743850" target="_blank">
            Statistical Models, Theory and Practice
           </a>
           ” by
           <a href="http://www.stat.berkeley.edu/~freedman/" target="_blank">
            David A. Freedman
           </a>
           , that I “donated” (the university is paying for it) to the library. I’m honored to be able to pay my tribute to him, who open my world of useful statistics.
          </p>
          <p>
           The firs time I met David was when I took his applied statistic class at Berkeley. At that time, I passed my Ph.D. qualify exam, started with some research projects and felt like I knew Statistics. In his class, I learned quickly that I knew NOTHING about Statistics except some abstract mathematical symbols.
          </p>
          <p>
           The first meeting of the class was the most wield period I have sit thought as a student. Several days before the first class, every student got his email in which a list of three papers were assigned for reading. We were good students so we all read the paper carefully, I assume at least. Then here came the first meeting of the class. David came in and explained several things about the course structures before we went to the more serious business, paper discussion.
          </p>
          <p>
           The discussion started like this. He calmly sit in a chair and asked “questions?”. Silence, …, silence, …, and longer silence. We had not expected that we were supposed to “initiate” the discussion instead of “participating”. Then he asked gain, “questions on the paper?”. We just sit there for more than 10 minutes, flipping through papers  and trying to find a meaning question to ask. Seems like we would sit there forever if we did not come up with any questions. It felt like the longest class I have ever taken.
          </p>
          <p>
           The format of the class kept the same way for the whole semester. Students first read the assigned papers and come up with questions about anything and everything about the paper. David entertained every question. The questions ranges from “why have the authors picked this model?” to “why have the authors NOT picked that model?”, from “Does the model fit the data well?” Do the data support the model at all?”, from “Does the evidence support the conclusion?” to “Is the evidence related to the conclusion?”. The interesting part is that about one third of the papers we discussed were written by him. We have to (at least try to) criticize the paper and he enjoys doing do as well. Sometime he would defend the paper for while and then add his own critics.
          </p>
          <p>
           Trying to recall what I have learned from the class, the most striking thing is that I cannot remember what models or methods we went over (there are a lot of them). I have to admit that I have a really bad memory. At the same time, I do remember one thing: Check the model assumptions and check them again and again.
          </p>
          <p>
           In an age of having so much computation power and advanced software packages to run almost any analysis in a short period time, our ability in drawing proper conclusion from data through mathematical inference is not necessarily improved unless we carefully check if we are using the right tools to answer the right questions. Thinking critically about each step of any analysis is the key to a proper conclusion. This is the first lesson I learned from David.
          </p>
          <p>
           [To be continued ……]
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